If in the summation formula n starts at n=n0 the starting index n0 is 2
The given series can be written as:
∑n=n0[infinity]an = (x-7)³/(x-7)⁶³* 2! + (x-7)⁹⁹/(x-7)¹²²⁷ * 3! + ...
We can simplify this expression by canceling out the common factor of (x-7) in each term of the series. This gives:
∑n=n0[infinity]an = (x-7)⁻⁶⁰ * 2! + (x-7)⁻¹¹²⁸ * 3! + ...
Now, we can see that each term in the series has the form:
an = [tex]k!/[(x-7)^{(3k-60)}][/tex]
where k is the index of the term and k ≥ 2, since the first two terms in the original series were combined into the first term of the simplified series.
Therefore, the starting index of the series is n0 = 2.
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I need help, please say the right answers!
A. Define variables and write an equation to represent the relationship between the quantities.
B. How far would the biker travel in 20 minutes?
C. If the biker traveled 48 miles, how many minutes did he bike? Round to the nearest tenth.
A. The equation d = s * t shows relationship between the quantities.
B. They would cover a distance of 10 miles in 20 minutes.
C. Rounded to the nearest tenth, the biker would bike for 96.0 minutes.
What is distance?
Distance is the measure of the physical space between two objects or points. It is a scalar quantity that is usually measured in units such as meters, kilometers, miles, etc. In physics, distance is considered to be a fundamental concept and is often used in conjunction with time to calculate other physical quantities, such as speed and acceleration.
a. We can define the following variables:
t: time in minutes
d: distance traveled by the biker in miles
s: speed of the biker in miles per minute
Using these variables, we can write the equation d = s * t to represent the relationship between them.
b. If the biker rides for 20 minutes, we can use the equation d = s * t to find the distance traveled. Assuming the biker's speed is 0.5 miles per minute, we get:
d = 0.5 * 20 = 10 miles
Therefore, the biker would travel 10 miles in 20 minutes.
c. If the biker traveled 48 miles, we can use the equation t = d / s to find the time taken, where s is again assumed to be 0.5 miles per minute:
t = 48 / 0.5 = 96 minutes
Rounded to the nearest tenth, the biker would have ridden for 96.0 minutes to cover 48 miles.
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Alyssa was comparing the price of chicken thighs at two stores. At SuperGrocery B, 3 pounds of chicken thighs costs $34.80. The table below represents the total cost, in dollars and cents, Y, that it costs for x pounds of chicken thighs at SuperGrocery A.How much more expensive is it, per pound, to buy chicken thighs at Store B than at Store A?
Pls Add A Picture : Will Update.
Write a statement that correctly describes the relationship between these two sequences: 18, 21, 24, 27, 30 and 6, 7, 8, 9, 10.
Each term in the second sequence is one-third of the corresponding term in the first sequence.
Each term in the second sequence is double the corresponding term in the first sequence.
Each term in the first sequence is one-third of the corresponding term in the first sequence.
Each term in the first sequence is double the corresponding term in the second sequence.
Each term in the second sequence is one-third of the corresponding term in the first sequence and is the statement that correctly describes the relationship between these two sequences: 18, 21, 24, 27, 30 and 6, 7, 8, 9, 10.
Each term in the second series is one-third of the equivalent term in the first sequence, which is the right way to characterize the relationship between the two sequences.
This means that for each term in the second sequence (6, 7, 8, 9, 10), the corresponding term in the first sequence (18, 21, 24, 27, 30) is three times larger. For example, the first term in the second sequence (6) is one-third of the first term in the first sequence (18), and the second term in the second sequence (7) is one-third of the second term in the first sequence (21), and so on.
It is important to note that the statement "Each term in the first sequence is double the corresponding term in the second sequence" is not correct, as this relationship does not exist between the two sequences.
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can yall pretty pls help me!!!!!!!!!!!!!!!
In the accompanying diagram, tangent PA and secant PBC are drawn to circle O from point P. If the measure of arc AC = 90° and the measure of arc AB = 26°, what is the m/P? plsss helps
The measure of angle P in the accompanying diagram is 0.072, when the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees. This is determined by using the formula for the measure of a central angle: M/P = (arc measure)/(360°).
What is angle?Angle is a measure of the amount of turn between two straight lines or planes that have a common point or line of intersection. It is usually measured in degrees, radians, or gradians. An angle can be measured in different ways, such as the angle between two lines, the angle between two planes, or the angle between two points. Angles are important in mathematics, engineering, and physics as they help describe the shape and size of objects.
Since the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees, we can use the formula for the measure of a central angle:
M/P = (arc measure)/(360°)
Therefore, the measure of angle P is:
M/P = (26°)/(360°) = 0.072
Therefore, the measure of angle P is 0.072.
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divide polynomials by a binomial (x² + 2x ÷ 1) ÷ (x + 1)
[tex]X+1-\frac{2}{x+1}[/tex]
Step-by-step explanation:
when we use the way like this because the 2 was left by it own at the end so we need to do like this, by we cannot divide it by x
steps for long division :Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder.
For numbers 5 - 6, fill in the boxes for the area method, and then put a check mark next to the correct answer.
(5 points per question: 1 point for each blank and 1 point for the correct answer). 5. Fill in the blanks within the area model for (4a - 2b)(12a + 6b) and then put a check next to the answer after simplifying (combining like terms).
4a
Answer: 12a + 6b
-2b
-8ab
Check: 48a^2 - 24b^2
Step-by-step explanation:
solve (1/27)^x=3^-4x+6 1) Rewrite the equation using the same base. 2) Solve for x. Remember to show all work.
PLEASE SHOW ALL WORK FOR BRAINLIEST
The equation can be rewritten using the same base as: 3⁻³ = 3⁻⁴ˣ⁺⁶.
The solution for x is: x = 9/4
How to rewrite the equation using the same base?
An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=).
1) To rewrite an equation using the same base, we need to apply the following property of exponents:
(1/27)ˣ = 3⁻⁴ˣ⁺⁶
(1/3³) = 3⁻⁴ˣ⁺⁶
3⁻³ = 3⁻⁴ˣ⁺⁶
2) We can equate the exponents and then solve for x. That is:
3⁻³ = 3⁻⁴ˣ⁺⁶
-3 = -4x + 6
4x = 6 + 3
4x = 9
x = 9/4
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Question 8 of 15
If a sample of 226 runners is taken from a population of 340 runners, the
population mean, u, is the mean of how many runners' times?
OA. 226
O B. 340
OC. Neither 226 nor 340
Therefore, the population mean, u, is the mean of 340 runners' times, regardless of the sample size. The correct answer is (B) 340.
What is mean?In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data, which represents the average value of the data. It is commonly known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of values.
Here,
The population mean, u, is the mean of the times for all 340 runners in the population. If a sample of 226 runners is taken from the population, then the mean of the sample will be an estimate of the population mean. However, the population mean itself is not affected by the size of the sample.
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help, and if you could explain how you got your value, domain and your range. thank you.
Answer: This is a quadratic function in standard form:
f(x) = x^2 - 10x + 9
The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
To rewrite the given function in vertex form, we need to complete the square:
f(x) = x^2 - 10x + 9
= (x - 5)^2 - 16
Now we can see that the vertex is at (5, -16) and the axis of symmetry is x = 5.
To find the x-intercepts, we set y = 0:
0 = (x - 5)^2 - 16
16 = (x - 5)^2
±4 = x - 5
x = 1 or x = 9
Therefore, the x-intercepts are (1, 0) and (9, 0).
To find the y-intercept, we set x = 0:
f(0) = 9
Therefore, the y-intercept is (0, 9).
The graph of the function is a parabola that opens upward with vertex at (5, -16), x-intercepts at (1, 0) and (9, 0), and y-intercept at (0, 9).
Step-by-step explanation:
the vertex is at (5, -16)
y-intercept is (0, 9).
the x-intercepts are (1, 0) and (9, 0).
axis of symmetry is x = 5
the range of the function is all real numbers greater than or equal to -16. In interval notation, we can write this as [-16, ∞).
the domain of the given function f(x) = x^2 - 10x + 9 is all real numbers.
what is the range of the function y= 2x + 3 when the domain is {-3, -1, 1}?
Answer:
Step-by-step explanation:
domain = x
range = y
when the domain is -1
y = 2(-1) - 3
y = -2 - 3
y = -5
range is -5
When the domain is 0
y = 2(0) - 3
y = 0 - 3
y = -3
range is -3
when the domain is 5
y = 2(5) - 3
y = 10 - 3
y = 7
range is 7
The range is { -5, -3, 7 }
Please show working out
Perimeter of quadrilateral: P = 20 m and Total area = 18 sq. m.
Explain about the quadrilaterals:Quadrilaterals have the following two qualities:
A closed quadrilateral should have four sides.A quadrilateral's internal angles add up to 360°.Using Pythagorean theorem in two given right triangles for finding the missing sides.
In triangle PQR
PR² = QR² + QP²
PR² = 8² + 1²
PR² = 64 + 1
PR = √65
Now,
In triangle PRS
PR² = PS² + RS²
PS² = PR² - RS²
PS² = 65 - 16
PS = 7
Perimeter of quadrilaterals:
P = sum of all exterior sides
P = 8 + 1 + 4 + 7
P = 20 m
Total area = area of triangle PQR + area of triangle PRS
Total area = 1/2 *QR*PQ + 1/2 * PS *SR
Total area = 1/2*8*1 + 1/2*7*4
Total area = 18 sq. m
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Male and female students were surveyed about dancing and playing sports. They had the following preferences:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.25 0.27 0.52
Female students 0.17 0.31 0.48
Column totals 0.42 0.58 1
Which of the following is a two-way conditional relative frequency table for gender?
Do you prefer dancing or playing sports?
Playing sports Dancing
Male students 0.60 0.47
Female students 0.40 0.53
Column totals 1 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 25% 27% 52%
Female students 17% 31% 48%
Column totals 42% 58% 100%
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 50 54 104
Female students 34 62 96
Column totals 84 116 200
The option that shows a two-way conditional frequency table is option B as shown in the image attached.
What is a two-way conditional frequency table?A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:
Gender.Preferred activity.Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.
Which option is correct?The correct option is option B because it meets the following requirements:
It displays the two variables: gender and preferred activities.It uses frequency values such as 0.48 rather than percentages or the number of people, which would be incorrect.The row totals are displayed in a third column than in a new row.8x+3y=-7 7x+2y=-3 solve by using elimination
Using elimination, the solution to the system of linear equations is x = -16/29 and y = -75/87.
What is a linear equation, exactly?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It is an algebraic equation that can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
Now,
To solve the system of equations 8x + 3y = -7 and 7x + 2y = -3 using elimination, we need to eliminate one of the variables by adding or subtracting the two equations.
One way to do this is to multiply the second equation by a suitable constant so that the coefficient of one of the variables is the negative of the corresponding coefficient in the first equation. In this case, if we multiply the second equation by 3, we can eliminate y by adding the resulting equation to the first equation:
8x + 3y = -7
(3)(7x + 2y = -3) -> 21x + 6y = -9
Adding the two equations, we get:
29x + 0y = -16
Simplifying, we get:
x = -16/29
Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:
8x + 3y = -7
Substituting x = -16/29, we get:
8(-16/29) + 3y = -7
Simplifying, we get:
-128/29 + 3y = -7
Multiplying both sides by 29, we get:
-128 + 87y = -203
Solving for y, we get:
y = -75/87
Therefore, the solution to the system of equations is x = -16/29 and y = -75/87.
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The function f(x) square root is compressed horizontally by a factor of 3 and , translated up 2 units. Write the equation of the transformed function.
The equation of the transformed function, after being compressed horizontally by a factor of 3 and translated up 2 units, is g(x) = sqrt(x/3) + 2.
If f(x) is a function, and we want to compress it horizontally by a factor of 3 and translate it up 2 units, we can apply the following transformations:
Horizontal compression by a factor of 3 means that we need to replace x with x/3 in the function.
Translation up 2 units means that we need to add 2 to the function.
The equation of the transformed function is g(x) = sqrt(x/3) + 2, which represents a function that has been compressed horizontally by a factor of 3 and translated up 2 units from the original function f(x) = sqrt(x).
Therefore, the equation of the transformed function is:
g(x) = sqrt(x/3) + 2
Note that g(x) represents the transformed function, and we have used the square root symbol to indicate that the function is the square root of x/3.
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An object has a mass of 175 g and a volume of 25 cm3.
Find the density of the object in g/cm3.
Cody has $700 in a savings account that pays 4% simple interest (l = prt). What is the amount of money Cody will have in his bank account after 2 years?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 700[1+(0.04)(2)] \implies A=700(1.08)\implies A = 756[/tex]
Un florero con forma cilíndrica tiene un diámetro interior de 12cm y su altura es de 25cm. Queremos llenarlo hasta los 2/3 de su capacidad. ¿Cuántos litros de agua necesitamos?
We need 3 liters of water to fill the cylinder up to 2/3 of its capacity.
The formula for the volume of a cylinder is V=π r2 h, where V is the volume, π is pi, r is the radius and h is the height. The radius of the cylinder is half of the diameter, so the radius of this cylinder is 6 cm, and the height is 25 cm. Applying the formula, the volume of the cylinder is V=π[tex]*6^2*25[/tex]
=4500π cm3.
To fill it up to 2/3 of its capacity, we need 3000π cm3 of water. To convert this to liters, we need to divide by 1000, so the answer is 3000π/1000=3 liters of water.
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What is the product if 32.9 is multiplied by the number represented by a decimal tiles below
The product of 32 and 0.9 is 28.8.
What is the product?The product of a set of numbers is the result of multiplying all the numbers together. For example, the product of 2, 3, and 4 is:
2 x 3 x 4 = 24
In general, if we have n numbers, the product is:
a1 x a2 x a3 x ... x an
where a1, a2, a3, ..., an are the individual numbers.
The product of two negative numbers is positive, while the product of a negative and a positive number is negative. The product of any number and 0 is always 0.
To find the product of 32 and 0.9, you can multiply these two numbers together:
32 x 0.9 = 28.8
Therefore, the product of 32 and 0.9 is 28.8.
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What is the value of x in the equation ½ x- Zy = 30, when y = 152
circle- note day 1
someone please solve this
Answer:
if i answered it would be 0
Step-by-step explanation:
Please help, my teacher refuses to explain how to do the math and I need this class to graduate.
-x^4+3x^2+2x+2
I need to find:
• Domain/Range
• Local Minimum/Maximum
• Intervals of Increase/Decrease
As x —> - ∞
As x —> ∞
Determine the x-intercepts
Determine the y-intercepts
I’m not sure what intervals of increase or decrease is, or what the “x —> ∞ stuff is either. I think all I can do is find the domain. Please help soon!
• Domain: All real numbers
• Range: (-∞, ∞)
• To find the local minimum/maximum and intervals of increase/decrease, we need to take the first and second derivatives of the function:
First derivative: -4x^3 + 6x + 2
Setting this equal to zero and solving for x, we get critical points at x ≈ -1.23, x ≈ 0.65, and x ≈ 1.23.
Second derivative: -12x^2 + 6
• At x ≈ -1.23, the second derivative is negative, so we have a local maximum.
• At x ≈ 0.65, the second derivative is positive, so we have a local minimum.
• At x ≈ 1.23, the second derivative is negative, so we have a local maximum.
• As x —> -∞, the function approaches ∞.
• As x —> ∞, the function approaches ∞.
• To find the x-intercepts, we set the function equal to zero and solve for x:
-x^4+3x^2+2x+2 = 0
This is a quartic equation that can be solved using various methods, such as factoring or using the quadratic formula. One solution is x ≈ -1.38. The other three solutions are complex numbers.
• To find the y-intercept, we set x = 0:
-y^4 + 2 = 0
Solving for y, we get y ≈ ±1.19. So the y-intercepts are (0, 1.19) and (0, -1.19).
Answer:
Domain- (−∞,∞),{x|x∈R}
Range- (−∞,17+6√3(over)4], {y∣y≤17+6√3(over)4}
Local Minimum/Maximum- (−1,2) is a local maxima
(1+√3(over)2 ,17+6√3(over)4) is a local maxima
(1−√3(over)2 ,17−6√3(over)4)is a local minima
Intervals of Increase/Decrease- Increasing on: (−∞,−1)(1−√3(over)2,1+√3(over)2)
Decreasing on: (−1,1−√3(over)2),(1+√3(over)2,∞)
Step-by-step explanation:
i hope this helps !
a researcher selects a sample and administers a treatment to the individuals in the sample. if the sample is used for a hypothesis test, what does the null hypothesis say about the treatment?
The null-hypothesis (H₀) in a two-tailed hypothesis test states that there is no significant difference between the treatment group and the control group, the correct option is (c)The treatment has no effect on scores.
The "Null-Hypothesis" assumes that any difference between the treatment group and control group is due to chance, and that treatment has no real effect on the outcome variable being measured.
The "Alternative-Hypothesis" (H₁) says that the treatment does have an effect on scores, but it does not specify whether the effect is positive or negative.
The null hypothesis is typically assumed to be true until there is sufficient evidence to reject it in favor of the alternative hypothesis.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a two-tailed hypothesis test, what does the null hypothesis (H₀) say about the treatment?
(a) The treatment increases scores.
(b) The treatment causes a change in scores.
(c) The treatment has no effect on scores.
(d) The treatment adds a constant to each score.
(e) The treatment decreases scores.
Which of the following are true statements about a 30-60-90 triangle?
Check all that apply.
A. The hypotenuse is 3 times as long as the longer leg.
B. The hypotenuse is twice as long as the longer leg.
C. The longer leg is twice as long as the shorter leg.
D. The longer leg is 3 times as long as the shorter leg.
E. The hypotenuse is twice as long as the shorter leg.
F. The hypotenuse is 3 times as long as the shorter leg.
Answer:
D. The longer leg is √3 times as long as the shorter leg.E. The hypotenuse is twice as long as the shorter leg.Step-by-step explanation:
You want to know which of the listed statements is true of a 30°-60°-90° triangle.
Side lengthsThe ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2.
This makes the following statements true:
D. The longer leg is √3 times as long as the shorter leg.E. The hypotenuse is twice as long as the shorter leg.how many gallons of pure acid should be added to 480 gallons of 22% acid solution to produce a solution that is 36%?
To produce 36% solution, 50 gallons of pure acid should be added to 480 gallons of 22% acid solution.
To solve the problem find out how many gallons of acid are there in the 22% solution
480*0.22= 105.6
Let the amount of pure acid required to produce 36% solution be x gallons.
So, the total amount of acid in the new solution will be
480 + x.
Write the equation for concentration:
(Total acid in the new solution)/ (Total volume of new solution) = 36/100
Using the above equation, we get;
[105.6+x]/[480+x] = 36/100
Cross multiply and simplify, we get;
3600 + 100x = 423.6 + 36x63.6x
= 3176.4x
= 3176.4/63.6x
x = 50
Therefore, the amount of pure acid required to produce 36% solution is 50 gallons.
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the city council has 6 men and 3 women. if we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? select the correct fractional response. hint: consider there is no replacement of an individual who is already selected.
The probability that the two chairpersons chosen are of the same gender is 9/36.
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It involves quantifying the likelihood of an event or outcome by assigning a numerical value between 0 and 1.
A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.
Probabilities between 0 and 1 indicate the likelihood of the event occurring, with higher probabilities indicating a greater likelihood.
This can be calculated by looking at the number of possibilities when selecting two members from a group of nine (6 men, 3 women):
Total possibilities = 9C2 = 9!/(2!*7!) = 9*8/2 = 36
Ways of selecting two of the same gender = 6C2 + 3C2 = 6*5/2 + 3*2/2 = 15
Therefore, the probability of selecting two of the same gender is 15/36, which reduces to 9/36.
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is 35/7 an integer or a non integer please help
Step-by-step explanation:
35/7 is an IMPROPER FRACTION .... it REDUCES to an INTEGER = 5
The fraction 35/7 equals to 5, which is an integer because it is a whole number without a fractional or decimal component.
Explanation:The fraction 35/7 equals to 5. The number 5 is a whole number that can be written without a fractional or decimal component, hence it is classified as an integer.
In general, an integer includes all whole numbers and their negative counterpart excluding fractions or decimals. Examples of integers are ...-3, -2, -1, 0, 1, 2, 3... and so on.
So the answer to your question is, 35/7 is an integer.
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Please help me answer the following question :)
Answer:
y = x - 1
Step-by-step explanation:
to determine the equation of the line we require to find the slope of the line and its y- intercept, where it crosses the y- axis.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0-(-1)}{1-0}[/tex] = [tex]\frac{0+1}{1}[/tex] = [tex]\frac{1}{1}[/tex] = 1
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = x - 1
Factor please!
2x² + x - 21
Answer: (x-3)(2x+7)
Step-by-step explanation:
Answer:
(2x + 7 )(x - 3)
Step-by-step explanation:
You can find the original expression by using the box method on the factors.
After giving 1/3 of his money to his wife and 1/4 of it to his mother, Jake still had $600 left. How much money did he give to his mother?
Let's start by setting up an equation to represent the problem.
Let's say Jake started with x amount of money.
After giving 1/3 to his wife, he has 2/3 left: (2/3)x
After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600
We can solve for x by isolating it:
(1/4)(2/3)x = $600
Multiplying both sides by 12/2 gives:
(2/3)x = $3600
Dividing both sides by 2/3 gives:
x = $5400
So Jake started with $5400.
To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:
(1/4)(2/3)($5400) = $900
So he gave his mother $900.
Step-by-step explanation:
x = original amount of money
the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.
x - (1/3)x - (1/4)x = 600
so let's bring every fractional term to .../12.
12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600
12x/12 - 4x/12 - 3x/12 = 600
5x/12 = 600
5x = 600×12
x = 600×12/5 = 120×12 = $1440
he gave to his mother
(1/4) × 1440 = $360